Anybody know the answer to this?

Question

100 people play a lottery, and each has a probability 0.02 of winning the jackpot. Each person spends 1 dollar to buy a ticket, so the lottery owners receive a total of 100 dollars. From this pool of 100 dollars, the winners are paid out as follows: if there are no winners, the owners do not pay out, so they net 100 dollars. If there is one winner, the owners pay them 50 dollars, and so they net 50 dollars. If there are two or more winners, the owners give their 100 dollars to all the winners to split equally, and so they net 0 dollars. Compute an approximate value for the expected net that the lottery owners make.

Answer 1

p (No winners) = 0.98¹⁰⁰

(call this p0)

p (1 winner) = 100 x 0.02 x 0.98 ⁹⁹

call this p1

p (2 or more winners) = 1 - p0 - p1

So expected net for the lottery owners = 100 p0 + 50 p1 + 0 (1-p0-p1) = 100 p0 + 50 p1

You can work this out